Calculus II

Course Code:

MATH 132

Course Period:

Spring

Course Type:

Core

Credits:

4

Theoric:

3

Practice:

2

Laboratory Hour:

0

ECTS:

6

Prerequisite Courses:

Calculus I

Course Objectives:

The aim of this course is to provide students with an understanding of sequences, series, analytic geometry in 3-space, limits and partial derivatives of functions of several variables, multiple integrals, line integrals of vector fields and their calculations.

Course Content:

Convergence of sequences. Convergence tests for series. Power, Taylor and Maclaurin series. Analytic geometry in 3-space. Functions of several variables, partial derivatives, extreme values. Double and triple integrals, change of variables. Vektör fields, line integrals, Green’s theorem.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination

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Course Learning Outcomes

Learning Outcomes	Program Outcomes	Teaching Methods	Assessment Methods
1) Knows the concepts of convergence of sequences and series and performs related calculations.	1	1,2	A
2) Knows the concepts of vectors, lines, planes and quadric surfaces in 3-space and performs related calculations.	1	1,2	A
3) Knows the concepts of double and triple integrals and some of their applications and performs related calculations.	1	1,2	A
4) Knows the concepts of line integrals and Green’s theorem and performs related calculations.	1	1,2	A

Course Flow

COURSE CONTENT
Week	Topics	Study Materials
1	Sequences and Convergence, Infiite Series	(From Textbook) 9.1,9.2
2	Convergence Tests for Positive Series, Absolute and Conditional Convergence	9.3,9.4
3	Power Series, Taylor and Maclaurin Series	9.5,9.6
4	Applications of Taylor and Maclaurin Series, Analytic Geometry in Three Dimensions, Vectors	9.7,10.1,10.2
5	The Cross Product in 3-Space, Planes and Lines	10.3,10.4
6	Quadric Surfaces, Functions of Several Variables, Limits and Continuity	10.5,12.1,12.2
7	Partial Derivatives, Higher-Order Derivatives, The Chain Rule	12.3,12.4,12.5
8	Linear Approximations, Differentials, Gradients and Directional Derivatives, Implicit Functions	12.6,12.7,12.8
9	Extreme Values, Extreme Values of Functions Defined, Restricted Domains, Lagrange Multipliers	13.1,13.2,13.3
10	Double Integrals, Iteration of Double Integrals in Cartesian Coordinates	14.1,14.2
11	Double Integrals in Polar Coordinates, Triple Integrals	14.4,14.5
12	Change of Variables in Triple Integrals	14.6
13	Line Integrals, Vector and Scalar Fields, Conservative Fields	15.3,15.1,15.2
14	Line Integrals of Vector Fields, Green's Theorem in the Plane	15.4,16.3

Recommended Sources

Textbook	R. A. Adams and C. Essex, Calculus, 7th Ed., Pearson (2010)
Additional Resources

Material Sharing

Documents
Assignments
Exams

Assessment

ASSESSMENT
IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	2	100
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE	1	40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM
No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.					X
2	Ability to identify, formulate, and solve Electrical and Electronics Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
3	Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose.
4	Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively.
5	Ability to design and conduct experiments, gather data, analyze and interpret results for investigating engineering problems
6	Ability to access information; For this purpose ability to perform database searching and conduct literature review.
7	Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
8	Ability to communicate effectively both orally and in writing; knowledge of a minimum of one foreign language.
9	Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
10	Awareness of professional and ethical responsibility.
11	Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
12	Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	6	84
Hours for off-the-classroom study (Pre-study, practice)	14	3	42
Mid-terms (Including self study)	2	8	16
Assignments
Final examination (Including self study)	1	12	12
Total Work Load			154
Total Work Load / 25 (h)			6.16
ECTS Credit of the Course			6

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Calculus II

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